Answer:
[tex]a_n = a_{n-1} (1.06) + 50[/tex]
Step-by-step explanation:
Suppose, [tex]a_0[/tex] is initial amount in the saving account,
Here, the annual interest rate is 6% and additional amount in each year is $ 50,
So, the amount after one year,
[tex]a_1 = a_0 + 6\%\text{ of }a_0 + 50 = a_0 + 0.06a_0 + 50 = a_0(1.06) + 50[/tex]
Amount after 2 years,
[tex]a_2 = a_1 + 6\%\text{ of }a_1 + 50 = a_1(1.06) + 50[/tex]
Amount after 3 years,
[tex]a_3 = a_2 + 6\%\text{ of }a_2 + 50 = a_2(1.06) + 50[/tex]
................................., so on....
Hence, by following the pattern,
The amount after n years,
[tex]a_n = a_{n-1} (1.06) + 50[/tex]
Which is the required recurrence relation for the amount of money in a savings account
